BdMO National Higher Secondary 2010/10

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
BdMO
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BdMO National Higher Secondary 2010/10

Problem 10:
\$a_1, a_2,\cdots , a_k, \cdots , a_n\$ is a sequence of distinct positive real numbers such that \$a_1 < a_2 < \cdots <a_k\$ and \$a_k > a_{k+1} > \cdots > a_n\$. A Grasshopper is to jump along the real axis, starting at the point \$O\$ and making \$n\$ jumps to the right of lengths \$a_1, a_2, \cdots , a_n\$ respectively. Prove that, once he reaches the rightmost point, he can come back to point \$O\$ by making \$n\$ jumps to the left of lengths \$a_1, a_2, \cdots , a_n\$ in some order such that he never lands on a point which he already visited while jumping to the right. (The only exceptions are point \$O\$ and the rightmost point)

Moon
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Re: BdMO National Higher Secondary 2010/10

"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

sourav das
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Re: BdMO National Higher Secondary 2010/10

Please check the link for solution: viewtopic.php?f=13&t=33&p=13138#p13138
You spin my head right round right round,
When you go down, when you go down down......
(-\$from\$ "\$THE\$ \$UGLY\$ \$TRUTH\$" )